Considere os vetores u⇒ = ( 3 , -1) e v⇒ = (-1 , 2) Assinale a alternativa que contém o vetor x⇒ = ( x, y ) de forma que tenhamos a igualdade 4(u-v)+1/3x=2u-x .
a) x⇒ = ( -15/2 , 15/2 )
b) x⇒ = ( 17/2 , - 15/2)
c) x⇒ = ( 15/2 , 15/2 )
d) x⇒ = ( 17/2 , 15/2 )
e) x⇒ = ( - 15/2 , - 15/2 )
Anexos:
Soluções para a tarefa
Respondido por
12
Boa tarde Roger!
Solução!
Vamos fazer um de cada pois o enunciado esta indicando coordenada (x,y) vez para obtermos o resultado.
![4(\vec{u})+ \dfrac{x}{3}=2(\vec{u})-x\\\\\\
4(3-(-1)+ \dfrac{x}{3}=2(3)-x\\\\\\\
4(3+1)+ \dfrac{x}{3}=2(3)-x\\\\\\\
4(4)+ \dfrac{x}{3}=6-x\\\\\\\
16+ \dfrac{x}{3}=6-x\\\\\\\
48+x=18-3x\\\\\\\
x+3x=18-48\\\\\\
4x=-30\\\\\
x= -\dfrac{30}{4}\\\\\\\
\boxed{x= -\dfrac{15}{2} }](https://tex.z-dn.net/?f=4%28%5Cvec%7Bu%7D%29%2B+%5Cdfrac%7Bx%7D%7B3%7D%3D2%28%5Cvec%7Bu%7D%29-x%5C%5C%5C%5C%5C%5C%0A4%283-%28-1%29%2B+%5Cdfrac%7Bx%7D%7B3%7D%3D2%283%29-x%5C%5C%5C%5C%5C%5C%5C%0A4%283%2B1%29%2B+%5Cdfrac%7Bx%7D%7B3%7D%3D2%283%29-x%5C%5C%5C%5C%5C%5C%5C%0A4%284%29%2B+%5Cdfrac%7Bx%7D%7B3%7D%3D6-x%5C%5C%5C%5C%5C%5C%5C%0A16%2B+%5Cdfrac%7Bx%7D%7B3%7D%3D6-x%5C%5C%5C%5C%5C%5C%5C%0A48%2Bx%3D18-3x%5C%5C%5C%5C%5C%5C%5C%0Ax%2B3x%3D18-48%5C%5C%5C%5C%5C%5C%0A4x%3D-30%5C%5C%5C%5C%5C%0Ax%3D+-%5Cdfrac%7B30%7D%7B4%7D%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Bx%3D+-%5Cdfrac%7B15%7D%7B2%7D+%7D+%0A%0A%0A "4(\vec{u})+ \dfrac{x}{3}=2(\vec{u})-x\\\\\\
4(3-(-1)+ \dfrac{x}{3}=2(3)-x\\\\\\\
4(3+1)+ \dfrac{x}{3}=2(3)-x\\\\\\\
4(4)+ \dfrac{x}{3}=6-x\\\\\\\
16+ \dfrac{x}{3}=6-x\\\\\\\
48+x=18-3x\\\\\\\
x+3x=18-48\\\\\\
4x=-30\\\\\
x= -\dfrac{30}{4}\\\\\\\
\boxed{x= -\dfrac{15}{2} }")
![4(\vec{v})+ \dfrac{y}{3}=2(\vec{u})-y\\\\\\\\
4(-1-2)+ \dfrac{y}{3}=2(-1)-y\\\\\\\
4(-3)+ \dfrac{y}{3}=-2-y\\\\\\\
-12+ \dfrac{y}{3}=-2-y\\\\\\\
-36+y=-6-3y\\\\\\
y+3y=36-6\\\\\
4y=30\\\\\
y= \dfrac{30}{4} \\\\\\\\
\boxed{y= \dfrac{15}{2}}](https://tex.z-dn.net/?f=4%28%5Cvec%7Bv%7D%29%2B+%5Cdfrac%7By%7D%7B3%7D%3D2%28%5Cvec%7Bu%7D%29-y%5C%5C%5C%5C%5C%5C%5C%5C%0A4%28-1-2%29%2B+%5Cdfrac%7By%7D%7B3%7D%3D2%28-1%29-y%5C%5C%5C%5C%5C%5C%5C%0A4%28-3%29%2B+%5Cdfrac%7By%7D%7B3%7D%3D-2-y%5C%5C%5C%5C%5C%5C%5C%0A-12%2B+%5Cdfrac%7By%7D%7B3%7D%3D-2-y%5C%5C%5C%5C%5C%5C%5C+%0A-36%2By%3D-6-3y%5C%5C%5C%5C%5C%5C%0Ay%2B3y%3D36-6%5C%5C%5C%5C%5C%0A4y%3D30%5C%5C%5C%5C%5C%0Ay%3D+%5Cdfrac%7B30%7D%7B4%7D++%5C%5C%5C%5C%5C%5C%5C%5C%0A%0A%5Cboxed%7By%3D+%5Cdfrac%7B15%7D%7B2%7D%7D+%0A "4(\vec{v})+ \dfrac{y}{3}=2(\vec{u})-y\\\\\\\\
4(-1-2)+ \dfrac{y}{3}=2(-1)-y\\\\\\\
4(-3)+ \dfrac{y}{3}=-2-y\\\\\\\
-12+ \dfrac{y}{3}=-2-y\\\\\\\
-36+y=-6-3y\\\\\\
y+3y=36-6\\\\\
4y=30\\\\\
y= \dfrac{30}{4} \\\\\\\\
\boxed{y= \dfrac{15}{2}}")
Boa tarde!
Bons estudos!
Solução!
Vamos fazer um de cada pois o enunciado esta indicando coordenada (x,y) vez para obtermos o resultado.
Boa tarde!
Bons estudos!
Usuário anônimo:
Muito obrigado amigo !!!
Perguntas interessantes